Uniformly Accelerated Motion

Introduction

A movement with uniformly increasing or decreasing speed is called uniformly accelerated motion .

Experiment

A car accelerates on a straight path. At certain points travel time and traveled distance are measured and recorded.

ResetStart

 $$s$$ in $$\rm m$$ $$t$$ in $$\rm s$$ $$v$$ in $$\rm \frac{m}{s}$$ $$a$$ in $$\rm \frac{m}{s^2}$$

Results

The distance-time curve is a parabola.

$$s = \dfrac{a}{2} \cdot t^2$$

The velocity-time curve is a straight line passing through the origin. This shows that the speed and the time are proportional to each other.

The proportionality constant is obviously the acceleration $$a$$ of the body.

$$v = a \cdot t$$

The acceleration-time curve is a straight line extending parallel to the x axis. This shows that the acceleration remains the same over the whole trip. The following applies:

$$a = \text{konst.}$$

Units of velocity

To specify the velocity the units $$\rm \frac{m}{s}$$ and $$\rm \frac{km}{h}$$ are often used. They can be converted into each other as follows:

$$\rm 1 \,\, \dfrac{km}{h} = \dfrac{1000 \,\, m}{3600 \,\, s} = \dfrac{5}{18} \dfrac{m}{s}$$
$$\rm 1 \,\, \dfrac{m}{s} = \dfrac{0,001 \,\, km}{\frac{1}{3600} \,\, h} = \dfrac{0,001 \cdot 3600}{1} \dfrac{km}{h} = 3,6 \,\, \dfrac{km}{h}$$

Sources

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